Question

As the temperature is increased, the time period of a pendulum

• A. increases as its effective length increases even though its centre of mass still remains at the centre of the bob
• B. decreases as its effective length increases even though its centre of mass still remains at the centre of the bob
• C. increases as its effective length increases due to shifting of centre of mass below the centre of the bob
• D. decreases as its effective length remains same but the centre of mass shifts above the centre of the bob

Answer 1

Answer: (A)

increases as its effective length increases even though its centre of mass still remains at the centre of the bob

Answer 2

Time period of the simple pendulum is $T=2\pi\sqrt{\frac{L}{g}}\quad\ldots\left(i\right)$ where $L$ is the effective length of the pendulum. With increase in temperature, the effective length $\left(L\right)$ of simple pendulum increases even though its centre of mass still remains at the centre of the bob.From $\left(i\right)$, $T \propto\sqrt{L}$ So $T$ increases as temperature increases.